The legislation includes new screening requirements that would effectively freeze the admittance of new refugees until the administration can verify that they aren't a threat to national security.

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While the Republican leader pledged to take up refugee legislation during early 2016, the timing of the vote comes after the Justice Department announced the arrest of two Iraqi-born Palestinians, who had entered the country as refugees, on terrorism-related charges.

The arrests sparked calls from House and Senate Republicans for the upper chamber to move legislation to crack down on accepting refugees, over concerns that terrorist groups could use the program to sneak into the United States.

"These votes will give all senators a chance to take a stand on the policy issues dominating the public debate — and Republicans a chance to stand with the frontrunner for their nomination," the Democratic leader said Thursday in a statement.

While it's unclear when Democrats will try to force a vote or what legislation they will use to advance the measure, the refugee proposal could give them an early chance to try to link a handful of vulnerable blue-state Republicans to Trump.

While Senate Republicans broadly dismissed Trump's push to ban Muslims from entering the country and have shown no signs of affection for Trump, they've also been reluctant to completely alienate him or his supporters.

If they are able to overcome Wednesday's hurdle, Republicans will also need 60 votes to end debate on the legislation.

Either way, the White House has threatened to veto the House bill, saying it creates "significant delays and obstacles in the fulfillment of a vital program that satisfies both humanitarian and national security objectives.”

Nominations

The Senate will also vote on Wilhelmina Marie Wright's nomination to be a U.S. district judge for the District of Minnesota on Tuesday evening.

Senators are expected to vote on the nomination at 5:30 p.m., after a half an hour of debate.

Democrats have repeatedly criticized Republicans for the pace of judicial nomination votes since they took control of the Senate last year. The Senate has confirmed 12 judges since January 2015.

"I’ve heard a lot of complaining about the pace of judicial nominations this Congress, but I believe actions speak louder than words," he added. "Furthermore, I’ve said this before but it bears repeating, there is no judicial vacancy 'crisis.'”

The vote on Wright's nomination is part of a deal reached last year to vote on five judicial nominations before the Senate's recess in mid-February.

Grassley added that the Judiciary Committee will also continue holding hearings on President Obama's nominees.

Republicans, however, are under pressure from outside groups to halt nomination votes. Heritage Action said Friday that the Senate should immediately stop confirming non-national security nominees.

"Senators should not grant unanimous consent to schedule any additional nomination votes," the group added.